Method for assessing an alpha particle emission potential of a metallic material

ABSTRACT

A method for assessing an alpha particle emission potential of a metallic material. A metallic material is initially subjected to a secular equilibrium disruption process, such as melting and/or refining, to disrupt the secular equilibrium of the radioactive decay of one or more target parent isotopes in the material. A sample of the material is treated to diffuse target decay isotopes within the sample such that the measured alpha particle emission directly corresponds to the concentration or number of target decay isotope atoms within the entirety of the sample, enabling the concentration of target decay isotopes in the sample to be determined. The concentration of target parent isotopes in the material may then be determined from the concentration of target decay isotopes and time elapsed from the secular equilibrium disruption process, and may be used to determine a maximum alpha particle emission that the metallic material will exhibit.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. patent application Ser. No.13/800,115, filed Mar. 13, 2013, which claims priority to U.S.Provisional Application No. 61/714,059, filed Oct. 15, 2012, U.S.Provisional Application No. 61/670,960, filed Jul. 12, 2012, U.S.Provisional Application No. 61/661,863, filed Jun. 20, 2012, and U.S.Provisional Application No. 61/642,787, filed May 4, 2012, each of whichare herein incorporated by reference in their entirety.

FIELD OF THE INVENTION

The present disclosure relates to metallic materials used in themanufacture of electronic components, and in particular, the presentdisclosure relates to a method for assessing an alpha particle emissionpotential of a metallic material of the type used in the manufacture ofelectronic components.

DESCRIPTION OF THE RELATED ART

Metallic materials, such as pure metals and metal alloys, for example,are typically used as solders in many electronic device packaging andother electronic manufacturing applications. It is well known that theemission of alpha particles from certain isotopes may lead tosingle-event upsets (“SEUs”), often referred to as soft errors or softerror upsets. Alpha particle emission (also referred to as alpha flux)can cause damage to packaged electronic devices, and more particularly,can cause soft error upsets and even electronic device failure incertain cases. Concerns regarding potential alpha particle emissionheighten as electronic device sizes are reduced and alpha particleemitting metallic materials are located in closer proximity topotentially sensitive locations.

Initial research surrounding alpha particle emission from metallicmaterials focused on lead-based solders used in electronic devicepackaging, and consequent efforts to improve the purity of suchlead-based solders. More recently, there has been a transition to theuse of non-lead or “lead free” metallic materials, such as silver, tin,copper, bismuth, aluminum, and nickel, for example, either as alloys oras pure elemental materials. However, even in substantially purenon-lead metallic materials, lead is typically present as an impurity,and such materials are often refined to minimize the amount of leadimpurities in the materials.

Uranium and thorium are well known as principal radioactive elementsoften present in metallic materials which may radioactively decayaccording to known decay chains to form alpha particle emittingisotopes. Of particular concern in non-lead materials is the presence ofpolonium-210 (²¹⁰Po) which is considered to be the primary alphaparticle emitter responsible for soft error upsets. Lead-210(²¹⁰Pb) is adecay daughter of uranium-238 (²³⁸U), has a half-life of 22.3 years, andβ-decays to bismuth-210 (²¹⁰Bi). However, due to the very short 5.01 dayhalf-life of ²¹⁰Bi, such isotope is essentially a transient intermediarywhich rapidly decays to ²¹⁰Po. The ²¹⁰Po has a 138.4 day half-life anddecays to the stable lead-206 (²⁰⁶Pb) by emission of a 5.304 MeV alphaparticle. It is the latter step of the ²¹⁰Pb decay chain, namely, thedecay of ²¹⁰Po to ²⁰⁶Pb with release of an alpha particle, that is ofmost concern in metallic materials used in electronic deviceapplications.

Although ²¹⁰Po and/or ²¹⁰Pb may be at least in part removed by meltingand/or refining techniques, such isotopes may remain as impurities in ametallic material even after melting or refining. Removal of ²¹⁰Po froma metallic material results in a temporary decrease in alpha particleemissions from the metallic material. However, it has been observed thatalpha particle emissions, though initially lowered, will typicallyincrease over time to potentially unacceptable levels as the secularequilibrium of the ²¹⁰Pb decay profile is gradually restored based onany ²¹⁰Pb remaining in the metallic material.

Problematically, whether an increase in alpha emissions of a metallicmaterial following a melting or refining process will eventually reachunacceptable levels is very difficult to assess and/or predict.

What is needed is a method of accurately assessing a level of alphaparticle emissions that a given metallic material will experience.

SUMMARY OF THE INVENTION

The present disclosure provides a method for assessing an alpha particleemission potential of a metallic material. A metallic material isinitially subjected to a secular equilibrium disruption process, such asmelting and/or refining, to disrupt the secular equilibrium of one ormore target parent isotopes in the material. A sample of the material istreated to diffuse target decay isotopes within the sample such that themeasured alpha particle emission directly corresponds to theconcentration or number of target decay isotope atoms within theentirety of the sample, enabling the concentration of target decayisotopes in the sample to be determined. The concentration of targetparent isotopes in the material may then be determined from theconcentration of target decay isotopes and time elapsed from the secularequilibrium disruption process, and may be used to determine a maximumalpha particle emission that the metallic material will exhibit.

In one form thereof, the present disclosure provides a method forassessing an alpha particle emission potential of a metallic material,the method including the steps of: detecting alpha particle emissionsfrom a sample of the metallic material; determining a concentration of atarget parent isotope in the sample of the metallic material from thealpha particle emissions detected in said detecting step and a timewhich has elapsed between said detecting step and a prior secularequilibrium disruption process; and determining a possible alphaemission of a target decay isotope of the target parent isotope from thedetermined concentration of the target parent isotope and the half-lifeof the target parent isotope.

In another form thereof, the present disclosure provides a method forassessing an alpha particle emission potential of a metallic material,the method including the steps of: subjecting a metallic material to asecular equilibrium disruption process; obtaining a sample of themetallic material following said subjecting step; detecting alphaparticle emissions from the sample; determining a concentration of atarget parent isotope in the sample from the alpha particle emissionsdetected in said detecting step and an elapsed time between saidsubjecting step and said detecting step; and determining a possiblealpha emission of a target decay isotope of the target parent isotopefrom the determined concentration of the target parent isotope and thehalf-life of the target parent isotope.

DETAILED DESCRIPTION

The present disclosure provides a method for assessing an alpha particleemission potential of a metallic material of the type typically used inthe manufacture of electronic components, such as metallic materialsused for solders, for example. The metallic material may be itself asingle or substantially pure elemental material, such as tin, lead,copper, aluminum, bismuth, silver, and nickel, for example, or may be analloy of any two or more of the foregoing materials or an alloy of anyone or more of the foregoing materials with one or more other elements.

The present method is principally described herein with reference to tinas the pure elemental material, and with reference to the ²¹⁰Pb decaychain by which ²¹⁰Po is the primary alpha particle emitter. However, thepresent method may also be used in connection with assessing alphaparticle emissions in other pure elemental materials and in alloys, andmay also be used to assess alpha particle emission from one or moreisotopes other than ²¹⁰Po formed from the ²¹⁰Pb decay chain.

As used herein, the term “target parent isotope” refers to an isotope ofinterest which is present in a metallic material and is able to decay toa daughter isotope, wherein the daughter isotope may subsequentlyalpha-decay, i.e., may decay to a further isotope with concomitantemission of an alpha particle. The term “target decay isotope”, as usedherein, refers to an isotope of interest which is a daughter isotope ofthe target parent isotope and itself may subsequently alpha-decay, i.e.,may decay to a further isotope with concomitant emission of an alphaparticle. The target decay isotope may or may not be itself a directdecay product of the target parent isotope. For example, if ²¹⁰Pb is atarget parent isotope, ²¹⁰Po may be a target decay isotope even though²¹⁰Pb decays to ²¹⁰Bi with subsequent decay of ²¹⁰Bi to ²¹⁰Po.

Although lead may be removed from a non-lead elemental material such astin, copper, aluminum, bismuth, silver, and nickel, for example, byrefining in order to reduce the amount of ²¹⁰Pb in the material andthereby the eventual alpha particle emissions, the amount of leadpresent in the material may still be potentially problematic in thecontext of alpha particle emissions even when the amount of lead is wellbeneath the detection limit of existing analytical methods for detectingindividual elements. For example, lead present as an impurity inmetallic materials may pose concern in the context of alpha particleemissions even at levels lower than parts per trillion by mass, which isbelow the detection limit of any existing analytical chemistry method.Therefore, even strenuous refining may not effectively remove ²¹⁰Pb toacceptable levels and, even where refining is known to be effective,existing analytical methods will typically be inadequate to detect any²¹⁰Pb remaining in a given metallic material following refining.Advantageously, the present method allows an amount, which as desiredmay be a maximum amount, of alpha particle emissions to be calculatedfor a given metallic material even when the amount of lead and/or otherradioactive impurities in the material are themselves present at levelsor concentrations well below the detection limit of any existinganalytical method.

According to the present method, the metallic material is subjected to asecular equilibrium disruption process. As used herein, the term“secular equilibrium disruption process” refers to a process to whichthe metallic material is subjected which at least partially disrupts thesecular equilibrium of the decay profile of at least one target parentisotope within the metallic material. In most instances, the secularequilibrium disruption process disrupts the secular equilibrium of thedecay profile of a target parent isotope by reducing the concentrationof the target parent isotope in the metallic material, by reducing theconcentration of a corresponding target decay isotope in the metallicmaterial, or by a combination of the foregoing. Exemplary secularequilibrium disruption processes include melting, casting, smelting,refining, or any combination of two or more of the foregoing processes.Exemplary refining processes include electro- or electro-chemicalrefining, chemical refining, zone refining, and vacuum distillation.Typically, in the secular equilibrium disruption process, andparticularly when the secular equilibrium disruption process is at leastin part a refining process, both the target parent isotopes and thetarget decay isotopes are at least partially removed as impurities orcontaminant components by physical and/or chemical separation from thebulk metallic material.

In some embodiments, the secular equilibrium disruption process mayremove substantially all of a given target decay isotope and therebyeffectively “reset” the secular equilibrium of the corresponding targetparent isotope. For example, in the case of a metallic materialincluding ²¹⁰Pb as a target parent isotope, the secular equilibriumdisruption process may substantially completely remove all of the ²¹⁰Potarget decay isotope in the material, such that the secular equilibriumof ²¹⁰Pb is effectively reset, wherein substantially all ²¹⁰Po that ispresent in the material following the secular equilibrium disruptionprocess is generated by decay of ²¹⁰Pb after the said disruptionprocess. However, the present process may also be practiced usingsecular equilibrium disruption processes that remove only a portion ofthe target parent isotope and/or target decay isotope, and the presentprocess is not limited to secular equilibrium disruption processes thatremove substantially all of a given target decay isotope.

In some embodiments, the secular equilibrium disruption process may becompleted in a relatively short amount of time and, in otherembodiments, the secular equilibrium disruption processes may require arelatively greater amount of time for completion, depending on thenature of the process and the number of processes that together mayconstitute the secular equilibrium disruption process. Therefore, theelapsed time discussed below, between the secular equilibrium disruptionprocess and the measurement of alpha particle emissions of the metallicmaterial, may be an elapsed time between the completion of the secularequilibrium disruption process (or processes) and the measurement ofalpha particle emissions of the metallic material.

After the metallic material is subjected to the secular equilibriumdisruption process, the alpha particle emission of the metallic materialis detected, i.e., an alpha particle emission measurement is obtained.Although it is within the scope of the present disclosure to obtain analpha particle emission of the entire metallic material in bulk form,typically a sample of the bulk metallic material will be obtained forpurposes of alpha particle emission analysis.

A relatively thin portion of the bulk metallic material may be obtainedas a sample by a suitable method such as rolling the bulk metallicmaterial to provide a thin sheet of sample material, or by any otheranother suitable method.

After the sample is obtained, the sample is treated by heat in order topromote diffusion of target decay isotopes in the sample material untilsuch point that the concentration of atoms of the target decay isotopesin the sample is uniform throughout the sample volume. In many samples,there may be a larger concentration of atoms of target decay isotopestoward the center of the sample, for example, or otherwise in otherareas of the sample such that a concentration mismatch or gradient ispresent. The heat treatment removes any such concentration mismatches orgradients by promoting diffusion of atoms of target decay isotopeswithin the sample from areas of relatively higher concentration towardareas of relatively lower concentration such that a uniformconcentration of target decay isotopes is obtained within and throughoutthe sample. When such uniform concentration is obtained, the number ofatoms of target decay isotopes within a detection limit depth of thealpha particle detection process will be representative of and, moreparticularly, will correlate directly to, the uniform concentration ofatoms of target decay isotopes throughout the entirety of the sample.Such uniform concentration is achieved when the chemical potentialgradient of the target decay isotopes is substantially zero and theconcentration of the target decay isotopes is substantially uniformthroughout the sample.

Stated in another way, at room temperature, the test sample may have achemical potential gradient, in that the concentration of target decayisotopes is higher on one side of the sample than another side of thesample, or at the centroid of the sample than at the outer surfaces ofthe sample. Heating of the sample adjusts the chemical potentialgradient and, at a sufficient time and temperature exposure, thechemical potential gradient is substantially zero and the concentrationof the target decay isotopes is substantially uniform throughout thesample.

As used herein, the term “detection limit depth” refers to a distancewithin a given metallic material through which an emitted alpha particlemay penetrate in order to reach a surface of the material and thereby bereleased from the material for analytical detection. Detection limitdepths for ²¹⁰Po in selected metallic materials are provided in Table 1below, in microns, which is based on the penetration of the 5.304 MeValpha particle released upon decay of ²¹⁰Po to ²⁰⁶Pb:

TABLE 1 Detection limit depths of ²¹⁰Po in selected metallic materialsDetection limit depth of Metallic material ²¹⁰Po (microns) Tin (Sn) 16.5Aluminum (Al) 23.3 Copper (Cu) 11 Bismuth (Bi) 17.1

The detection limit depth for alpha particles of differing energy, suchas alpha particles emitted upon radioactive decay of alphaparticle-emitting isotopes other than ²¹⁰Po, will vary, with thedetection limit depth generally proportional to the energy of the alphaparticle. In the present method, emitted alpha particles may be detectedby use of a gas flow counter such as an XIA 1800-UltraLo gas ionizationchamber available from XIA L.L.C. of Hayward, Calif. according themethod described by JEDEC standard JESD 221.

Target decay isotopes such as ²¹⁰Po are known to diffuse or migratewithin metallic materials and, in this respect, the heat treatment ofthe present method is used to promote diffusion of the target decayisotope within the material sample to eliminate concentration gradients.In particular, target decay isotopes, such as ²¹⁰Po, will have adiffusion rate J in a given metallic material, which can be expressedaccording to equation (1) below:

$\begin{matrix}{J = {{- D}\frac{\partial\varphi_{Po}}{\partial x}}} & (1)\end{matrix}$

wherein: ∂φ/∂x is the concentration gradient of the target decayisotope, such as ²¹⁰Po, and D is the diffusion coefficient. Theconcentration gradient of the target decay isotope is determined bymeasuring the alpha particle emissions at the surface of a sample,removing a layer of material of x thickness, such as by chemicaletching, and measuring the alpha particle emissions at the x depth. Theconcentration of the target decay isotope at the original surface and atdepth x is directly proportional to the alpha particle emission at eachsurface, and concentration gradient of the target decay isotope iscalculated as the difference between the concentration at one of thesurfaces and the concentration at depth x over the distance x.

To determine the polonium diffusion rate J, the polonium alpha particleemissions from 5-5.5 MeV in a tin sample was measured. The sample wasthen heated at 200° C. for 6 hours, and the alpha particle emissionmeasurement was repeated. The number of polonium atoms N is calculatedfrom equation (2) below:

N=A/λ _(Po)  (2)

wherein:A is the alpha particle emission measured in counts/hr; andΔ_(Po)=ln 21138.4 days, based on the half-life of ²¹⁰Po.

The number of moles of polonium was calculated by dividing the number ofpolonium atoms N by Avogadro's number. Dividing the difference in thenumber of moles of polonium by the sample area (0.1800 m²) and the timeover which the sample was heated (6 hours) yields a lower bound on thediffusion rate of 4.5×10⁻²³ mol·m⁻²·s⁻¹ at 473K in tin.

TABLE 2 Data for diffusion rate determination Measurement A (Counts/Hr)N (atoms) Moles Initial 24.75 1.19E+05 1.97E−19 Final 46.71 2.24E+053.72E−19

Based on equation (1), one may determine a suitable time and temperatureheating profile to which the sample may be exposed in order to diffusethe target decay isotope within the sample sufficiently to eliminate anyconcentration gradients, such that detection of alpha particle emissionswithin the detection limit depth of the sample is representative, anddirectly correlates, to the concentration of the target decay isotopethroughout the sample. For example, for a tin sample having a thicknessof 1 millimeter, a heat treatment of 200° C. for 6 hours will ensurethat any concentration gradients of ²¹⁰Po atoms within the sample areeliminated.

Thus, for a given metallic material and sample size, the application ofheat may be selected and controlled by time and temperature exposure ofthe sample to ensure that atoms of a target decay isotope are diffusedto a sufficient extent to eliminate concentration gradients. It has beenfound that, by the present method, in providing a suitable time andtemperature profile for the heat treatment step, measurement of alphaparticle emissions from a target decay isotope present within thedetection limit depth directly corresponds to the concentration ornumber of target decay isotope atoms within the entirety of the sample.

It is generally known that subjecting a metallic material to heatpromotes diffusion of elements within the material. However, priormethods have employed heat treatment simply to increase the number ofalpha particle emissions detected over background levels to therebyincrease the signal to noise ratio of the alpha particle emissiondetection.

The alpha particle emissions attributable to ²¹⁰Po is expressed aspolonium alpha activity, A_(Po), at a time (t) following the secularequilibrium disruption process. From the A_(Po) and elapsed time (t),the concentration of ²¹⁰Pb atoms in the sample can be calculated usingequation (3):

$\begin{matrix}{\left\lbrack {\,^{210}{Pb}} \right\rbrack_{0} = {\frac{\lambda_{Po} - \lambda_{Pb}}{\lambda_{Po}{\lambda_{Pb}\left( {^{{- \lambda_{Pb}}t} - ^{{- \lambda_{Po}}t}} \right)}}\left( {{A_{Po}(t)} + {{A_{Po}\left( t_{0} \right)}^{{- \lambda_{Po}}t}}} \right)}} & (3)\end{matrix}$

wherein:A_(Po)=ln 2/138.4 days, based on the half-life of ²¹⁰Po;A_(Pb)=ln 2/22.3 years (8,145.25 days) based on the half-life of ²¹⁰Pb;andtime (t) is the time which has elapsed between the secular equilibriumdisruption process and the alpha particle emission measurement.

Due to the fact that ²¹⁰Pb has a 22.3 year half-life, the ²¹⁰Pbconcentration is substantially constant over the time (t) when the time(t) is less than three years, particularly where the alpha particleemission measurement occurs relatively soon after the secularequilibrium disruption process. Also, when substantially all of the²¹⁰Po is removed in the secular equilibrium disruption process (whichmay be the case when the secular equilibrium disruption process is astrenuous refining process, for example) the last term in equation (3)above is very near to zero because the initial ²¹⁰Po concentration willbe very near to zero when the alpha particle emissions are measuredrelatively soon after the secular equilibrium disruption.

The concentration of the target parent isotope may be calculated by theabove-equation (3) and, once the concentration of the target parentisotope is calculated, the known half-life of the target parent isotopemay be used to provide an assessment or prediction of a maximumconcentration of the target decay isotope within the material based onthe re-establishment of the secular equilibrium profile of the targetparent isotope.

In other words, once the concentration of ²¹⁰Pb atoms is determinedusing equation (3), based on the half-life of ²¹⁰Pb the maximum ²¹⁰Poactivity at re-establishment of secular equilibrium will occur at(t)=828 days, and is calculated from equation (4) below:

$\begin{matrix}{{A_{Po}\left( {t = {828\mspace{14mu} d}} \right)} = {{\frac{\lambda_{Pb}\lambda_{Po}}{\lambda_{Po} - \lambda_{Pb}}\left\lbrack {\,^{210}{Pb}} \right\rbrack}_{0}\left( {^{{- \lambda_{Pb}}828\mspace{14mu} d} - ^{{- \lambda_{Po}}828\mspace{14mu} d}} \right)}} & (4)\end{matrix}$

Consistent time units (i.e., days or years) should be used acrossequation (3) and equation (4).

The maximum ²¹⁰Po activity directly correlates to a maximum alphaparticle emission of the material, and will occur at 828 days from thesecular equilibrium disruption process. In this manner, due to the factthat the present method will typically be carried out relatively soonafter the secular equilibrium disruption process, the calculated maximumconcentration of the target decay isotope and concomitant alpha particleemission will typically be a maximum future concentration of the targetdecay isotope and concomitant alpha particle emission that the metallicmaterial will exhibit over a timeframe which corresponds to thehalf-life of the target parent isotope.

For example, based on the half-life of ²¹⁰Pb, the applicable timeframeor “window” by which a maximum possible concentration of ²¹⁰Po (andthereby a peak in alpha particle emissions) will be reached in thematerial will occur at 828 days (27 months) from the secular equilibriumdisruption process.

It is also possible to calculate a possible concentration of ²¹⁰Po (andthereby the alpha particle emissions) at any specified elapsed time fromthe secular equilibrium disruption process. In this manner, it ispossible to calculate a possible concentration of ²¹⁰Po after asufficient elapsed time from the secular equilibrium disruption process,where the sufficient elapsed time may be at least 200, 250, 300, 350 or365 days from the secular equilibrium disruption process. For example,based on the half-life of ²¹⁰Pb, the applicable timeframe by which the²¹⁰Po concentration will reach 67% of the maximum possible concentrationin the material will occur at 200 days from the secular equilibriumdisruption process. Similarly, the ²¹⁰Po concentration will reach 80%and 88% of the maximum possible concentration in the material at 300days and 365 days, respectively, from the secular equilibrium disruptionprocess.

Advantageously, according to the present method, after a metallicmaterial has been subjected to a secular equilibrium disruption processsuch as by refining the metallic material, a maximum alpha particleemission that the metallic material will reach during the useful life ofthe material may be accurately predicted. In this manner, the presentmethod provides a valuable prediction of the maximum alpha particleemission for metallic materials, such as solders, that are incorporatedinto electronic devices.

EXAMPLES

The following non-limiting Examples illustrate various features andcharacteristics of the present invention, which is not to be construedas limited thereto.

Example 1 Determination of Maximum Alpha Emissions in Refined TinSamples

The present method was used to assess the maximum potential alphaemissions in eight refined tin samples. The tin samples were refinedaccording to the method disclosed in U.S. Provisional Patent ApplicationSer. No. 61/661,863, entitled Improved Refining Process for ProducingLow Alpha Tin, filed on Jun. 20, 2012. Test samples of the refined tinsamples were obtained by cutting an approximately 1 kilogram sample froman ingot and rolling the sample to a thickness of 1 millimeter. The testsamples were heated at 200 C for six hours, and the alpha particleemissions of the test samples were measured using an XIA 1800-UltraLogas ionization chamber available from XIA L.L.C. of Hayward, Calif. Themeasured alpha particle emissions and elapsed times between refining andthe measurement of alpha particle emissions are shown below in Table 3.

TABLE 3 Refined tin sample data Elapsed time (t) between Maximumrefining and ²¹⁰Pb alpha Alpha particle measurement of concentrationparticle emissions alpha particle at time = 0 emission (alpha flux)emissions (atoms/cm²) (equation Sample (counts/hr/cm²) (days) (equation(2)) (3)) 1 0.002 89 66 0.0056 2 0.0045 258 74 0.0063 3 0.0016 113 440.0037 4 0.004 272 64 0.0055 5 0.0016 211 29 0.0025 6 0.0009 32 720.0061 7 0.025 553 324 0.0276 8 0.0195 523 255 0.0217

From the measured alpha particle emission and the elapsed time (t)between refining and the measurement of alpha particle emission, theconcentration of ²¹⁰Pb at (t)=0 can be calculated from equation (3)above.

For example, the alpha particle emission of Sample 1 was measured at0.002 counts/hr/cm² at 89 days from refining. Based on equation (3)above, the number of ²¹⁰Pb atoms per cm2 ([²¹⁰Pb]₀) needed to generatethe measured ²¹⁰Po activity, i.e., measured alpha particle emission, wascalculated to be 66. Using equation (4) above, the activity or predictedalpha particle emission of ²¹⁰Po at (t)=828 days was calculated as0.0056 counts/hr/cm².

In Sample 7, the alpha particle emission was measured at 0.025counts/hr/cm² at 523 days from refining. The value of [²¹⁰Pb]_(c), wascalculated based on equation (3) to be 255 atoms/cm², and the maximumalpha particle emission was calculated based on equation (4) as 0.0217counts/hr/cm².

As may be seen from Samples 1 and 7, the difference between the measuredalpha particle emission and the calculated maximum alpha particleemission decreases as time (t) approaches 828 days, with the greaterdifference for Sample 1 attributable to the alpha particle emissionmeasurement being obtained early in the secular equilibrium cycle beforesecular equilibrium could be re-established after refining.

Example 2 Determination of Time Required to Diffuse the Target DecayIsotope

The time required to diffuse the target decay isotope in a tin samplewas investigated. Tin samples were refined according to the methoddisclosed in U.S. Provisional Patent Application Ser. No. 61/661,863,entitled Improved Refining Process for Producing Low Alpha Tin, filed onJun. 20, 2012. A test sample of the refined tin sample was obtained bycutting a sample from an ingot and rolling the sample to a thickness of0.45 millimeter. The test sample was heated at 200° C. for one hour, andthe alpha particle emissions of the test samples were measured using anXIA 1800-UltraLo gas ionization chamber available from XIA L.L.C. ofHayward, Calif. Measurement of the alpha particle emissions requiredabout 24 hours, after which the sample was again heated for one hour at200° C. and the alpha particle emissions were measured. This process(e.g., one hour heat treatment followed by measurement of alpha particleemissions) was repeated for a total of five heat/measurement cycles. Themeasured alpha particle emissions and the total hours at which thesample was heated at 200° C. are shown below in Table 4.

TABLE 4 Determination of the target decay isotope diffusion data Totalhour(s) Alpha particle emissions sample heated (alpha flux)(counts/hr/cm²) 0 0.017 1 0.025 2 0.024 3 0.027 4 0.025 5 0.026

As can be seen from Table 4, the activity or alpha flux of the sampleincreased from 0.017 counts/hr/cm² to 0.025 counts/hr/cm² after one hourat 200° C. That is, the activity or alpha flux of the tin sampleincreased more than 50% after one hour at 200° C. As further shown inTable 4, there was no significant change in the activity or alpha fluxof the sample when heated for more than one hour at 200° C., suggestingthat one hour at 200° C. was sufficient to achieve a substantiallyuniform concentration of the target decay isotopes throughout thesample.

Example 3 Determination of Diffusion of Target Decay Isotopes in CopperSamples

The present method was used to assess the maximum potential alphaemissions in a copper sample. The copper sample was electrolyticallyrefined from 99.99% to 99.9999% purity. After refinement, the purifiedcopper was heated and molded into an ingot.

A test sample of a copper material was obtained by cutting a sample fromthe ingot and rolling the sample to a thickness of 3.2 mm. The alphaparticle emissions of the test sample were measured using an XIA1800-UltraLo gas ionization chamber available from XIA L.L.C. ofHayward, Calif., before and after heating the copper test sample for sixhours at 200° C.

Prior to heating, the copper test sample had an activity or alpha fluxof 0.0036 counts/hr/cm², and after heating at 200° C. for six hours, thecopper test sample had an activity of 0.0051 counts/hr/cm². This exampleillustrates that heating promotes the diffusion of target decay isotopesin the copper material. The maximum alpha particle emissions for thecopper sample calculated from Equation 4 above was 0.05 counts/hr/cm².

While this invention has been described as having a preferred design,the present invention can be further modified within the spirit andscope of this disclosure. This application is therefore intended tocover any variations, uses, or adaptations of the invention using itsgeneral principles. Further, this application is intended to cover suchdepartures from the present disclosure as come within known or customarypractice in the art to which this invention pertains and which fallwithin the limits of the appended claims.

What is claimed is:
 1. A method for assessing an alpha particle emissionpotential of a bulk material, said method comprising the steps of:detecting alpha particle emissions from a sample of the bulk material;determining a concentration of ²¹⁰Pb in the sample from the alphaparticle emissions detected in said detecting step and a time which haselapsed between said detecting step and a prior secular disruptionprocess; and determining a possible alpha emission of ²¹⁰Po from thedetermined concentration of ²¹⁰Pb and a half-life of ²¹⁰Pb.
 2. Themethod of claim 1, wherein the time which has elapsed is an elapsed timebetween said detecting step and a completion of a prior secularequilibrium disruption process.
 3. The method of claim 1, furthercomprising the additional steps, prior to said detecting step, of:obtaining a sample of the bulk material; and heating the sample todiffuse atoms of ²¹⁰Po within the sample until a uniform concentrationof ²¹⁰Po is obtained throughout the sample.
 4. The method of claim 1,wherein the secular equilibrium disruption process comprises at leastone process selected from the group consisting of melting, refining, andcombinations of the foregoing.
 5. The method of claim 1, wherein saidstep of determining a possible alpha emission of ²¹⁰Po comprisesdetermining a maximum possible alpha emission of ²¹⁰Po.
 7. A method forassessing an alpha particle emission potential of a bulk material, saidmethod comprising the steps of: detecting alpha particle emissions froma sample of the bulk material; adjusting the chemical potential gradientof the sample; determining a concentration of a target parent isotope inthe sample from the alpha particle emissions detected in said detectingstep and a time which has elapsed between said detecting step and aprior secular equilibrium disruption process; and determining a possiblealpha emission of a target decay isotope of the target parent isotopefrom the determined concentration of the target parent isotope and thehalf-life of the target parent isotope.
 8. The method of claim 7,wherein the target parent isotope is ²¹⁰Pb.
 9. The method of claim 7,wherein the target parent isotope is ²¹⁰Pb and the target decay isotopeis ²¹⁰Po.
 10. The method of claim 7, wherein said step of determining apossible alpha emission of a target decay isotope comprises determininga maximum possible alpha emission of the target decay isotope.
 11. Themethod of claim 7, wherein said step of determining a possible alphaemission of a target decay isotope comprises determining a possiblealpha emission of the target decay isotope at at least 300 days fromcompletion of the secular equilibrium disruption process.
 12. The methodof claim 7, wherein the secular equilibrium disruption process removessubstantially all the target decay isotope in the sample.
 13. The methodof claim 7, wherein said adjusting step comprises heating the sample todiffuse atoms of the target decay isotope within the sample until thechemical potential gradient of the sample is substantially zero.
 14. Themethod of claim 7, wherein the secular equilibrium disruption processcomprises at least one process selected from the group consisting ofmelting, refining, and combinations of the foregoing.
 15. A method forassessing an alpha particle emission potential of a bulk material, saidmethod comprising the steps of: subjecting the bulk material to asecular equilibrium disruption process by melting; obtaining a sample ofthe bulk material following said subjecting step; forming a uniformconcentration of atoms of a target decay isotope throughout the sample;detecting alpha particle emissions from the sample; determining aconcentration of a target parent isotope in the sample from the alphaparticle emissions detected in said detecting step and an elapsed timebetween said subjecting step and said detecting step; and determining apossible alpha emission of the target decay isotope of the target parentisotope from the determined concentration of the target parent isotopeand the half-life of the target parent isotope.
 16. The method of claim15, wherein the elapsed time between said subjecting step and saiddetecting step is an elapsed time between completion of said subjectingstep and said detecting step.
 17. The method of claim 15, wherein saidforming step comprises heating the sample to diffuse atoms of the targetdecay isotope within the sample until a uniform concentration of atomsof the target decay isotope is obtained throughout the sample.
 18. Themethod of claim 15, wherein the target parent isotope is ²¹⁰Pb and thetarget decay isotope is ²¹⁰Po.
 19. The method of claim 15, wherein saidstep of determining a possible alpha emission of a target decay isotopecomprises determining a maximum possible alpha emission of the targetdecay isotope.
 20. The method of claim 15, wherein said step ofdetermining a possible alpha emission of a target decay isotopecomprises determining a possible alpha emission of the target decayisotope at at least 300 days from completion of the secular equilibriumdisruption process.